Most hostings provide some space consumption info in some form in their administration panels (since they limit space provided). If you want this in and via WordPress please elaborate on details a bit.
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Rarst♦Oct 11 '12 at 17:35

I have used the same recursive method myself. It adds up the space used and counts the number of files nicely. But on the WP-MU site that I am managing many of the users have allocated disk space up to and over 1gB and over 10,000 files. To be able to charge the right sum my system has to perform periodic disk scans and on these big accounts it appears that the processing exceeds my ISPs processing limits. So when the tight recursive loop has finished the process bails out and skips the little finishing part where blog id, space and date are supposed to be stored in the usage log. My only option then is to implement a 'bit by bit' - logic, or upgrade my web hotel. That is expensive, and the first option requires programming of a kind that I would like to avoid.